相关论文: Dynamical Systems on Leibniz Algebroids
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincar\'e…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
Two types of higher order Lie $\ell$-ple systems are introduced in this paper. They are defined by brackets with $\ell > 3$ arguments satisfying certain conditions, and generalize the well known Lie triple systems. One of the…
We analyze the semiclassical limit of spectral theory on manifolds whose metrics have jump-like discontinuities. Such systems are quite different from manifolds with smooth Riemannian metrics because the semiclassical limit does not relate…
In this study, Clifford Kaehler analogue of Lagrangian dynamics is introduced. Also,the some geometrical and physical results over the obtained Clifford Kaehler dynamical systems are discussed.
We define a higher analogue of Dirac structures on a manifold M. Under a regularity assumption, higher Dirac structures can be described by a foliation and a (not necessarily closed, non-unique) differential form on M, and are equivalent to…
Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems such as gradient and metriplectic systems with constraints.…
In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra $R=\mathbb{C}[\partial]V$ through three algebraic operations on $V$ are…
This paper introduces and investigates the structure of $\delta$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $\delta$. The authors define $\delta$-Lie algebras, $\delta$-Lie…
We give an explicit solution to the problem of differentiation of hyperelliptic functions in genus 4 case. We describe explicitly the polynomial Lie algebras and polynomial dynamical systems connected to this problem.
We study geometric representation theory of Lie algebroids. A new equivalence relation for integrable Lie algebroids is introduced and investigated. It is shown that two equivalent Lie algebroids have equivalent categories of infinitesimal…
A general procedure of affinization of linear algebra structures is illustrated by the case of Leibniz algebras. Specifically, the definition of an affine Leibniz bracket, that is, a bi-affine operation on an affine space that at each…
We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, using a result on the reduction modulo primes of systems of…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…
The commutative semiring $\mathbf{D}$ of finite, discrete-time dynamical systems was introduced in order to study their (de)composition from an algebraic point of view. However, many decision problems related to solving polynomial equations…
In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…